Present progressive parallelism
I have a three part question: 1) "After eating this meal"
I translate it as "Despues de comiendo esta comida"
The book translates it as "Despues de comer esta comida"
Why isn't comer conjugated?
2) In addition, this phrase doesn't seem to have parallelism, and I'm not sure why. "...but I'm dreaming about playing my guitar"
I translate it as "pero sonando sobre tocando mi guitarra"
The book translates it as "pero sonando con tocar mi guitarra.
3) In 2) when do you use sobre and when do you use con to translate "about"?
4 Answers
You'll probably found the info contained in this reference article helpful 
As a noun English nouns that end in -ing are expressed using infinitives, not gerunds in Spanish.
Me gusta hablar español. (I like speaking Spanish.) Ver es creer. (Seeing is believing.) Correr es bueno para la salud. (Running is good for your health.)
As an adjective English adjectives that end in -ing are also expressed using infinitives or other conjugated verbs, not gerunds in Spanish.
Tengo los zapatos de correr. (I have running shoes.) ¿De quién es el bebé que llora? (Whose is this crying baby?)
1.) The infinitive is acting like a noun in this case, the infinitive after a preposition is a pretty common construction.
Después de comer= After eating [After to eat]
Antes de llorar= Before crying [Before to cry]
The infinitive in Spanish also takes the same meaning when the verb acts as a noun. Basically, when you can fit the infinitive instead of a gerund and the sentence makes grammatical sense, then the infinitive is used
No se permite nadar en este lago. =Swimmimg [to swim] is not allowed...
2.) Soñar con means "To dream about..". It's a Spanish construction that, when translated literally, makes no sense; however, it is grammatically correct and must be memorized in this way.
There aren't many other instances where "con" is used over "sobre" or "de," (at least not many that I know of.)
Rather than the gerund (-ing) Use the infinitive as the object of a preposition or as the subject of a verb:
Después de descansar = “after resting”
Leer es divertido = “Reading is fun”
"Soñar con" always go together as a team.
"Después de" always go together at a team.
Después de" always go together at a team. - Mariana
Nearly always 
- for instance here's some examples of when después means then or after(wards) and doesn't require the 'de'
Después no lo he vuelto a ver.
I haven't seen him since then.
Y después fui al cine.
And after(wards) I went to the movies.
